Solve for all values of xx by factoring.x, squared, minus, 11, x, plus, 22, equals, minus, 2x 2 −11x+22=−2
Question
Solve for all values of xx by factoring.
x, squared, minus, 11, x, plus, 22, equals, minus, 2
Solution
The equation you've given is x^2 - 11x + 22 = -2.
First, let's simplify this equation by moving -2 to the other side of the equation. This gives us:
x^2 - 11x + 22 + 2 = 0
Which simplifies to:
x^2 - 11x + 24 = 0
Next, we factor the quadratic equation. We're looking for two numbers that multiply to 24 and add to -11. Those numbers are -8 and -3. So, we can write the equation as:
(x - 8)(x - 3) = 0
Setting each factor equal to zero gives the solutions to the equation:
x - 8 = 0 => x = 8
x - 3 = 0 => x = 3
So, the solutions to the equation x^2 - 11x + 24 = 0 are x = 8 and x = 3.
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